Two key Senate Republicans delivered mixed messages today over whether they’re prepared to resolve a standoff with Democrats over extending the Social Security payroll tax cut, which is set to expire Jan. 1.

Both Senate Minority Leader Mitch McConnell (Ky.) and Sen. Lindsey Graham (S.C.) said on Sunday talk shows that Republicans want to extend the tax cut and will find a way to do it. But both also touted a House GOP plan that extends the cut but includes controversial riders that Democrats have said they will reject.

“I believe that we should extend the payroll tax holiday another year and avoid a tax increase in working people for another year,” McConnell said on “Fox News Sunday.” He predicted that the House GOP proposal will pass both the House and the Senate “on a bipartisan basis.”

Speaking on NBC’s “Meet the Press,” Graham also expressed optimism that the extension would win approval: “At the end of the day, the payroll tax [cut] will get extended as it is now. And we’ll find a way to pay for it in a bipartisan fashion.”

But the GOP plan would require President Barack Obama to clear the way for work to begin on the proposed Keystone XL pipeline, which would run between Canada and Texas. Both Obama and Senate Majority Leader Harry Reid (D-Nev.) have said they would reject any bill that includes the pipeline provision. McConnell called the pipeline a “shovel-ready project” that “would create 20,000 jobs immediately, almost with no money.”

Graham acknowledged that “the pipeline is not going to sell.” It remains unclear how Republicans will win over Democratic support for a plan that includes the pipeline provision.

Democrats have accused Republicans of being more concerned about millionaires than about the middle class. Senate Democrats had wanted to pay for the payroll tax cut extension with a fractional surtax on those earning $1 million or more a year.

“If Congress fails to extend the payroll tax cut, it’s a new tax and an added tax for average working people next year,” Senate Majority Whip Dick Durbin (D-Ill.) said on “Meet the Press.” He added, “This is a make-or-break moment for the middle class.”

McConnell rejected the argument that the GOP approach favors millionaires.

“This is a very balanced package,” he said. “It doesn’t do anything to millionaires. In fact, it actually goes after them on the benefits side.”

Like Graham, McConnell predicted the extension would eventually pass. “Obviously, we’ll reach an agreement,” he said. “The president is posturing here. He had to stand up to the AFL-CIO. I’m on the same side as Jimmy Hoffa and the AFL-CIO on this. The Teamsters and the AFL-CIO want the Keystone pipeline right now.”

McConnell and Graham also defended Senate Republicans’ filibuster to block a vote last week on Obama’s nomination of former Ohio Attorney General Richard Cordray as the first director of the Consumer Financial Protection Bureau, the Wall Street oversight agency created by the Dodd-Frank financial reform law. Republicans had wanted to condition Cordray’s installation on reforms that would put a multi-person board, not a single director, at its head and put Congress in charge of overseeing it.

“This new agency answers to no one, absolutely no one — another unelected czar,” McConnell said. “We’ve got a bunch of those in the White House. We don’t need any more of them.” He added that the problem lies not with Cordray but with the structure of the agency.

“It’s one individual who could bring down the banking system in this country if he chose to, has unlimited power,” McConnell said. “No one has that kind of power.”